Question

Is y=2x +5 a direct variation and if so, what is the constant?

Answer 1

`y=2x+5` is not a direct variation

Explanation:

To be a direct variation, multiplying either variable by some amount must cause the other variable to be multiplied by exactly the same amount.

For the example `y=2x+5`
We can see that if `x=color(blue)(2)` then `y=color(green)(9)`

If we multiplied `x` by `color(red)(3)` (i.e. `x=color(blue)(2)xxcolor(red)(3)=color(brown)(6)`)
then
if `x` and `y` were in direct variation
the value of `y` would need to become `color(green)(9)xxcolor(red)(3)=color(purple)(21)`

but we can see that `y=2*(color(brown)(6)) + 5 = 17 !=color(purple)(21)`